Expression of type Conditional

from the theory of proveit.core_expr_types.tuples

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional
from proveit.core_expr_types import a_1_to_i, b_1_to_j, c_1_to_k, d_1_to_j
from proveit.logic import Equals

# build up the expression from sub-expressions
expr = Conditional(Equals([a_1_to_i, b_1_to_j, c_1_to_k], [a_1_to_i, d_1_to_j, c_1_to_k]).with_wrapping_at(2), Equals([b_1_to_j], [d_1_to_j]))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left\{\begin{array}{c} \begin{array}{l} \left(a_{1}, a_{2}, \ldots, a_{i},b_{1}, b_{2}, \ldots, b_{j},c_{1}, c_{2}, \ldots, c_{k}\right) =  \\ \left(a_{1}, a_{2}, \ldots, a_{i},d_{1}, d_{2}, \ldots, d_{j},c_{1}, c_{2}, \ldots, c_{k}\right) \end{array} \end{array} \textrm{ if } \left(b_{1}, b_{2}, \ldots, b_{j}\right) = \left(d_{1}, d_{2}, \ldots, d_{j}\right)\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 4 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	8, 9
6	ExprTuple	10, 12, 11
7	ExprTuple	10, 13, 11
8	ExprTuple	12
9	ExprTuple	13
10	ExprRange	lambda_map: 14 start_index: 20 end_index: 15
11	ExprRange	lambda_map: 16 start_index: 20 end_index: 17
12	ExprRange	lambda_map: 18 start_index: 20 end_index: 21
13	ExprRange	lambda_map: 19 start_index: 20 end_index: 21
14	Lambda	parameter: 31 body: 22
15	Variable
16	Lambda	parameter: 31 body: 23
17	Variable
18	Lambda	parameter: 31 body: 24
19	Lambda	parameter: 31 body: 25
20	Literal
21	Variable
22	IndexedVar	variable: 26 index: 31
23	IndexedVar	variable: 27 index: 31
24	IndexedVar	variable: 28 index: 31
25	IndexedVar	variable: 29 index: 31
26	Variable
27	Variable
28	Variable
29	Variable
30	ExprTuple	31
31	Variable